#13215: Skew polynomials
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Reporter: caruso | Owner: tbd
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.1
Component: experimental package | Resolution:
Keywords: skew polynomials | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: #13214 | Stopgaps:
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Changes (by caruso):
* dependencies: => #13214
Old description:
> If R is a ring equipped with an endomorphism sigma, the ring of skew
> polynomials over (R,sigma) is the ring of usual polynomials over R with
> the modified multiplication given by the rule X*a = sigma(a)*X.
>
> Skew polynomials play an important role in several domains like coding
> theory or Galois representations theory in positive characteristic.
>
> The attached patch provides:
>
> 1. a basic implementation of skew polynomials over any commutative ring
> (including addition, multiplication, euclidean division, gcd...)
> 1. a more complete implementation of skew polynomials over finite fields
> (including factoring)
New description:
If R is a ring equipped with an endomorphism sigma, the ring of skew
polynomials over (R,sigma) is the ring of usual polynomials over R with
the modified multiplication given by the rule X*a = sigma(a)*X.
Skew polynomials play an important role in several domains like coding
theory or Galois representations theory in positive characteristic.
The attached patch provides:
1. a basic implementation of skew polynomials over any commutative ring
(including addition, multiplication, euclidean division, gcd...)
1. a more complete implementation of skew polynomials over finite fields
(including factoring)
NB: This ticket depends on ticket #13214 which implements Frobenius
endomorphisms over finite fields. For convenience, I reattach the
corresponding patch here.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13215#comment:2>
Sage <http://www.sagemath.org>
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